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http://dx.doi.org/10.4134/CKMS.2013.28.3.589

DENSE SETS IN WEAK STRUCTURE AND MINIMAL STRUCTURE  

Modak, Shyamapada (Department of Mathematics University of Gour Banga)
Publication Information
Communications of the Korean Mathematical Society / v.28, no.3, 2013 , pp. 589-596 More about this Journal
Abstract
This paper is an attempt to study and introduce the notion of ${\omega}$-dense set in weak structures and the notion of m-dense set in minimal structures. We have also investigate the relationships between ${\omega}$-dense sets, $m$-dense sets, ${\sigma}({\omega})$ sets, ${\pi}({\omega})$ sets, $r({\omega})$ sets, ${\beta}({\omega})$ sets, m-semiopen sets and $m$-preopen sets. Further we give some representations of the above generalized sets in minimal structures as well as in weak structures.
Keywords
GTS; m-dense set; m-semiopen set; m-preopen set; ${\omega}$-dense set;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
연도 인용수 순위
1 M. Alimohammady and M. Roohi, Fixed point in minimal spaces, Nonlinear Anal. Model. Control 10 (2005), no. 4, 305-314.
2 M. Alimohammady and M. Roohi, Linear minimal spaces, Chaos Solitons Fractals 33 (2007), no. 4, 1348-1354.   DOI   ScienceOn
3 A. Csaszar, Generalized open sets, Acta Math. Hungar. 97 (1997), no. 1-2, 65-87.
4 A. Csaszar, Generalized topology, generalized continuity, Acta Math. Hungar. 96 (2002), no. 4, 351-357.   DOI   ScienceOn
5 A. Csaszar, Weak structures, Acta Math. Hungar. 131 (2011), no. 1-2, 193-195.   DOI
6 M. Ganster, Preopen sets and resolvable spaces, Kyungpook Math. J. 27 (1987), no. 2, 135-142.
7 N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly 70 (1963), 36-41.   DOI   ScienceOn
8 H. Maki, J. Umehara, and T. Noiri, Every topological space is pre T1/2, Men. Fac. Sci. Kochi Univ. Ser. A Math. 17 (1996), 33-42.
9 A. S. Mashhour, M. E. AbD El-Mosef, and S. N. El-Deeb, On precontinuous and weak precontinuous mappings, Proc. Math. Phys. Soc. Egypt 53 (1982), 47-53.
10 W. K. Min, m-semiopen sets and M-semicontinuous functions on spaces with minimal structures, Honam Math. J. 31 (2009), no. 2, 239-245.   과학기술학회마을   DOI   ScienceOn
11 W. K. Min, On minimal semicontinuous functions, Commun. Korean Math. Soc. 27 (2012), no. 2, 341-345.   과학기술학회마을   DOI   ScienceOn
12 W. K. Min and Y. K. Kim, On minimal precontinuous functions, J. Chun. Math. Soc. 22 (2009), no. 4, 667-673.
13 W. K. Min and Y. K. Kim, m-preopen sets and M-precontinuity on spaces with minimal structures, Adv. Fuzzy Sets Syst. 4 (2009), no. 3, 237-245.
14 O. B. Ozbakir and E. D. Yildirim, On some closed sets in ideal minimal spaces, Acta. Math. Hungar. 125 (1009), no. 3, 227-235.